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We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This result is then used to analyze the average error correcting performance of codes that are randomly drawn from unitarily… (More)

We present a proof for the quantum channel coding theorem which relies on the fact that a randomly chosen code space typically is highly suitable for quantum error correction. In this sense, the proof is close to Shannon's original treatment of information transmission via a noisy classical channel. In the theory of information transmission the information… (More)

We consider quantum error correction of quantum noise that is created by a local interaction of qubits with a common bosonic bath. The possible exchange of bath bosons between qubits gives rise to spatial and temporal correlations in the noise. We find that these kinds of noise correlations have a strong negative impact on quantum error correction.

To operationalize social status epidemiology of social inequalities in health uses uncompounded indices, as school and job education, income and occupational status. Social epidemiology describes social inequalities from a more comprehensive perspective, including indicators of social status as well as subjective attitudes and behavior. Examples of a study… (More)

We formulate and prove an exact relation which expresses the moments of the two-point conductance for an open disordered electron system in terms of certain density correlators of the corresponding closed system. As an application of the relation, we demonstrate that the typical two-point conductance for the Chalker-Coddington model at criticality… (More)

Within a generalized Caldeira-Leggett model, we analyze the conditions under which a bosonic heat bath can entangle two microscopic quantum systems at a distance r. We find that the attainable entanglement is extremely distance-sensitive. Significant entanglement can only be achieved if the systems are within a microscopic distance that is of order of the… (More)

We consider thermalization of a microscopic quantum system by interaction with a thermal bath. Our interest is the minimal size the bath can have while still being able to thermalize the system. Within a specific thermalization scheme, we show that a single spin 1/2 can be fully thermalized by interaction with a bath that consists of just two other spins… (More)